A mathematical model for fluoride uptake by the skeleton.

A mathematical model was developed that predicts fluoride accumulation and clearance from the skeleton based upon fluoride bioavailability, bone remodeling rate, and the fluoride binding characteristics of bone. It was assumed that fluoride binds to bone in a nonlinear fashion such that a smaller percentage of fluoride is bound to bone if fluoride intake is increased to high levels. Bone resorption rate was assumed to be proportional to the solubility of hydroxyfluoroapatite which is inversely related to bone fluoride content. The predictions made by the model compared favorably with experimental results from fluoride uptake and clearance studies. Parametric studies done using the model showed the following: (1) fluoride can be cleared from the skeleton by bone remodeling, but fluoride clearance takes over four times longer than does fluoride uptake; and (2) fluoride uptake by the skeleton was positively associated with bone remodeling rate. However, the concentration of fluoride in newly formed bone does not decrease with reduced remodeling rates and surpasses 10,000 ppm for intakes of fluoride greater than 9 mg/day. For osteoporosis, daily dose and duration of fluoride treatment should be selected to avoid reaching a toxic cumulative bone fluoride content.